public class Test03 {
    public int[][] matrixBlockSum(int[][] mat, int k) {
        int m = mat.length , n = mat[0].length;
        int[][] dp =  new int[m+1][n+1];
        for(int i = 1 ; i <= m; i++){
            for(int j = 1 ; j <= n ;j++){
                dp[i][j] = dp[i-1][j] + dp[i][j - 1] - dp[i-1][j - 1] + mat[i-1][j - 1];
            }
        }

        //使用dp
        int ret[][] = new int[m][n];
        for(int i = 0 ; i < m;i++){
            for(int j = 0; j<n ;j++){
                int x1 = Math.max(0, i - k) + 1, y1 = Math.max(0,j - k) + 1;
                int x2 = Math.min(m -1 , i + k) + 1, y2 = Math.min(n -1 , j +k) + 1;
                ret[i][j] = dp[x2][y2] - dp[x1 -1][y2] - dp[x2][y1-1] + dp[x1-1][y1-1];
            }
        }
        return ret;
    }
}
